By using the test function method, combining properties of the Heisenberg Laplace operator and K function, and utilizing relevant differential inequality techniques, we studied the rupture problem of the initial value problem solutions for  a class of wave equations (systems) with convolution terms and weak damping terms in n-dimensional space. The results show that there is no global weak solution to the problem when the initial value satisfies certain assumptions. This obtained result gives the influence of parameters in the convolution term on rupture of the solution, and provided a reference for the study of existence of solutions to wave equations (systems) with weak damping and convolution type nonlinear terms in high dimensional spaces.

The author  investigated a class of abstract non-autonomous impulsive evolution equations in Banach spaces and proved the
 Lipschitz pseudo-orbit shadowing property for the problem under relatively weak conditions by using the contraction mapping principle. The obtained results are not only applicable to specific cases, but also have universality for general equations.

By using the local linking theorem in critical point theory and the theory of variable exponent Sobolev space, the author proved the existence of nontrivial solutions for Kirchhoff-type equation with p(x)-Laplacian operator without  assuming  the  (AR) type superlinearity condition held.

By using prior estimates and differential inequality technique, the author discussed the influence of base perturbations on the stability of heat conduction inside a semi infinite cylinder. The author proves that as the disturbance amplitude decreases, the solution converges exponentially to the solution corresponding to a completely flat base. This result has certain theoretical significance for  the robustness of heat conduction model and the potential impact of small geometric irregularities on heat transfer prediction.

The author considers  the existence of positive solutions for the boundary value problems of a class of singular second-order ordinary differential equations. Based on the Krasnoselskii fixed point theorem, the author  proves that there exists a constant λ₀>0, such that the problem has at least one positive solution when λ∈(0,λ₀).

Let R be a ring, and S be a multiplicative subset of R. Firstly, we introduce the notion of Gorenstein u-S-injective modules by mean
s of the theory of Hom functors. Secondly, we study the homological properties of Gorenstein u-S-injective modules by using the u-S-Five Lemma and the method of constructing pull-back diagrams. Particalarly, it is shown that an R-module M is Gorenstein u-S-injective if and only if Extⁱ_R(E,M) is u-S-torsion module for any u-S-injective R-module E and any integer i>0, and M admits a proper left u-S-injective-resolution. The class of Gorenstein u-S-injective modules is closed under finite direct sums.

Let R be a ring, and S be a multiplicative subset of R. Firstly, based on the u-S-flat modules, we introduce the concept of Gorenstein u-S-flat modules,  and  use the long exact sequence theorem and the properties of u-S-flat modules to study the homological properties of Gorenstein u-S-flat modules, and give equivalent characterizations of Gorenstein u-S-flat modules. Secondly, we  prove that the class of Gorenstein u-S-flat modules is projective solvable class if and only if it is closed with respect to extensions.

Let T be a formal triangular matrix ring, where R and S are associative rings with identity element, C is a faithfully semidualizing (S,R)-bimodule. It is showed that: 1) M is a Ding C-projective left S-module; 2) N is Ding C-injective left R-module. The obtained conclusions establish links between Ding C-modules and Ding modules through T.

Let n be a positive integer and R be an associative ring with identity. Firstly, the definition of n-Tor-pair over the ring R is introduced. Secondly, some properties of n-Tor-pairs are given, and hereditary n-Tor-pairs are discussed. Finally, the equivalent characterization of the direct product of modules in X having finite X-projective dimension is given when (X,Y) is an n-Tor-pair.

We constructed 4 order unitary matrices by using tensor product based on three classes of 2 order unitary matrices. The results show  that the complete sets of the mutually unbiased bases are still mutually unbiased under four classes  of unitary transformations, but the complete sets of the mutually unbiased bases are no longer mutually unbiased under the other five classes of unitary transformations. The sum of l₁ norm of coherence of Bell-diagonal states under the four-dimensional mutually unbiased bases is no more than 9.

By constructing the edge-coloring and total-coloring algorithms based on the characteristic trees,  combined with combinatorial analysis, we obtain that the adjacent vertex distinguishing multiplicative edge chromatic number of Halin graphs is not more than 3, and the adjacent vertex distinguishing multiplicative total chromatic number of Halin graphs is 2. The  results show that the adjacent vertex distinguishing multiplicative 1-2-3 conjecture and multiplicative 1-2 conjecture are valid for Halin graphs, respectively.

Firstly, we introduced the W operator on harmonic Bergman space and gave the concept of slant Toeplitz operators.  Secondly, we studied the spectral structure and compactness of the W operator, and gave the integral representation of slant Toeplitz operators, which  provided a theoretical basis for subsequent research on  the compactness and boundedness of slant Toeplitz operators.

Let S be a ring, and H(S) be the quaternion ring on S. We consider the (m,n)-Jordan centralizers and (m,n)-Lie centralizers on the quaternion ring. By using the generator analysis method, we prove that the (m,n)-Jordan centralizers are standard centralizers, a
nd the (m,n)-Lie centralizers are standard Lie centralizers.

Firstly, by using  the divergence theorem and  geometric analysis methods, we  studied the rigidity problem of compact η-Ricci-Bourguignon solitons, and obtained two key integral formulas for  the potential vector field of the soliton and the dual vector field of η. Secondly, under different integral conditions, we obtain rigidity results of the soliton, which  proves that the soliton is either an η-Einstein manifold or an Einstein manifold.

Aiming at the problem of  the information overload caused by the explosion of big data teaching resources and the insufficient accuracy of traditional retrieval-augmented generation (RAG) in multi-source information fusion, we proposed a big data knowledge learning method based on GraphRAG. Firstly, we designed a Chinese prompt template to drive GraphRAG to automatically extract course entities and relationships, constructed an initial knowledge graph, and persisted it to Neo4j graph database. Secondly, through entity alignment and relationship completion, manually organized knowledge points were integrated with the automatically constructed graph to form a unified and evolving knowledge graph database. Finally, the community summaries pre generated by GraphRAG were utilized to achieve global semantic search, while relying on the Neo4j graph database to achieve precise local retrieval of knowledge points. The experimental results show that the proposed method is significantly better than traditional RAG in terms of question answering accuracy, response correlation, and smoothness of multi\|source information integration.

Aiming at the problem that  deepfake  detection algorithms  had low detection effect on neural texture (NT) forgery methods in FaceForensics++(FF++) dataset,  we  proposed a reverse knowledge distillation network (RKD-Net) by improving  fine-grained feature extraction of face images. Firstly, the RKD-Net used  reverse knowledge distillation (RKD) as the main framework, 
preserving  the rich fine-grained information of the input face images. Secondly, spatial and channel reconstruction convolution (SCConv) was inserted between the encoder and the decoder to enhance the representation of fine-grained information from both spatial and channel dimensions. Finally, a residual coordinate attention (RCA) classifier was used to enhance the real and detailed features  output by  the reverse knowledge distillation network, and classify the face images input to the network according to these different features. The experimental results  show that RKD-Net achieves  the best detection effect of NT forgery methods  
while guaranteeing the  detection effect of  other  forgery methods.

Aiming at the problems existing in the process of face image posture correction, such as ignoring detailed features, blurring the texture of the face image after correction, and excessive gap between the face features and the identity features of the original image, we proposed a face correction method based on the dual discriminator and dual attention mechanism of the generative adversarial network. Firstly, while using the dual discriminator to determine the face identity and face posture, we designed a face representation attention module to enhance the overall features of the face, prevented the loss of face-related information, and improved the model’s ability to perfect face images. Secondly, we designed an adaptive edge-enhanced attention module. By using the adaptive attention mechanism and Sobel filter, the edge detail features and key features of the face were enhanced to generate a frontal face with realistic facial features and contours. Finally, a new normalization layer CrossNorm was adopted to improve the robustness under distribution changes,  and the results of testing  experiments on the Multi-PIE dataset and the CFP dataset show that the proposed model generates frontal face images with better face correction effects compared to the comparison model.

Aiming at the problem of complex image content, diverse action postures, and significant background interference in the task of sports image classification,  we proposed a sports image classification algorithm based on an improved ResNet50 model. Firstly,  a squeeze-and-excitation module was embedded within the residual structure to adaptively enhance key channel features and improve feature expression capability. Secondly, on this basis, a feature pyramid network was introduced to achieve effective fusion of multi-scale features, and enhance the model’s perception ability of objects at different scales. Finally, classification prediction was performed through global average pooling and  fully connected layers. Experimental results show  that the classification accuracy of the proposed method is about  5% higher than that of the conventional ResNet50 model, fully demonstrating  its robustness and superiority in handling complex actions and diverse backgrounds. The experimental results  not only validate the effectiveness and feasibility of the proposed method,  but also provide more reliable technical support and practical reference for applications in sports video analysis,  intelligent sports training and other related fields.

Aiming at  the problems that the traditional K-Means algorithm was sensitive to initial centroids, prone to local optima, and failing to fully mine the potential semantic features of clustering results, we proposed a  K-Means clustering algorithm based on heuristic crossover strategy optimization. Firstly, the algorithm used  a density-driven heuristic crossover initialization strategy to screen representative parent points in high-density regions, and  introduced a crossover coefficient to dynamically generate diverse initial centroids to  reduce the volatility of clustering results caused by random initialization. Secondly, during the clustering iteration process, by combining the information of parent points with the intra-cluster mean update rule, the centroid positions were dynamically adjusted through crossover operations, which solved the problem of inter-cluster overlap caused by the local optima of the traditional algorithm. Finally, the optimized clustering results were input into a multi-layer perceptron, which utilized its nonlinear mapping ability to mine potential features and  achieved  deep fusion of clustering results with  deep semantic features. Experimental results show that the contour coefficient, Davies-Bouldin index, and adjusted Rand index of the algorithm reach 0.634, 1.398 and 0.621, respectively, which are significantly superior to other improved algorithms, effectively improving clustering accuracy, stability, and interpretability of the algorithm.

Aiming at the problem  that traditional spectral clustering-based subspace clustering methods were prone to outlier interference and thus show degraded clustering performance when there were outliers in high-dimensional data, we proposed an active block diagonal subspace clustering method based on automatic weighting. The method first assigned a corresponding weight to each data point, identified outliers in the data through weight differences, then actively reduced its contribution in the representation matrix to construct a better representation matrix and improved the  clustering performance of the model. Experimental results on 10 datasets compared with 8  algorithms show that the average clustering accuracy, normalized mutual information, and adjusted Rand index of the proposed method are generally better than the comparison algorithms on datasets with 10% or 20% outliers. It performs the best or ranks in the top three on more than half of the datasets in general clustering tasks. Therefore,  the method can not only efficiently handle high-dimensional data clustering with outliers, but also maintain competitiveness in general clustering tasks, providing an effective solution to enhance the robustness of high-dimensional data clustering and having high practical application value.

Aiming at the problem of underutilization of job locality and  low prediction accuracy in high-performance computing systems, we  proposed a job runtime prediction algorithm considering locality. The algorithm comprehensively utilized the global and local features of job log data, and improved prediction accuracy through a voting mechanism that combined with machine learning prediction and locality-based time-series prediction. Experimental results show that on actual scheduling log datasets such as 
 Unliu Gaia and PIK IPLEX, the JRPL algorithm outperforms or is not inferior to the machine learning algorithms  as the baseline in all  three  metrics: average absolute error, average prediction accuracy, and hit rate. This research result provides an improved prediction model for job scheduling in high-performance computing systems, which hepls to make more accurate execution time forecasting, improve system resource utilization, and reduce computational costs.

Aiming at the problem that the search space of the traveling salesman problem (TSP) grew exponentially with the increase of the number of cities, making it difficult for the algorithm to traverse all possible paths in a limited time, and was susceptible to the accumulation of pheromones during the search process, leading to premature convergence to local optimal solutions. In order to quickly converge to high-quality solutions when solving TSP, we proposed an analysis method for solving  TSP problem of  dual population ant colony algorithm based on path contribution evaluation. Firstly, we established a TSP mathematical model in the form of a weighted graph. Secondly,  two independent populations were introduced for parallel search: One population used an elite ant system to update pheromones, quickly converged using existing information, and obtained the shortest path of TSP; the other population used a strengthening  sub path evaluation mechanism to update pheromones,  jumped out of the local optimal solution by searching for new solution spaces, and  obtained the shortest path of TSP. Thirdly, by comparing and analyzing the shortest paths of the two populations, the shortest path with the smaller value was obtained as the global optimal path. Finally, introducing a path contribution evaluation mechanism to update the pheromones of the two populations again, we obtained the final TSP solution. Experimental results  show that this method can effectively solve and analyze TSPs of different scales. It can not only shorten the length of the path, but also obtain the shortest path that traverses all cities and returns to the starting point, and the data distribution effect is better.

Aiming at the multi-depot vehicle routing problem with time windows, we constructed a model with the goal of minimizing total cost,  proposed an improved dung beetle optimizer algorithm based on multi-strategy, and solved it. By introducing a hierarchical system to update rolling dung beetles, it established communication with top-tier beetles to enhance the algorithm’s search capability. Differential variation was designed to perturb the positions of reproductive dung beetles and  reduce the likelihood of getting stuck in local optima. Probability-driven random foraging behavior was devised for foraging dung beetles, enabling them to randomly explore broader search spaces to find potential optimal solutions. Adversarial learning was using to generate reverse 
solutions for thief dung beetles, increasing the probability of finding better candidate solutions and strengthening the algorithm’s optimization capability. This algorithm was using to solve the multi-depot vehicle routing  problem with time windows. Comparative experiments with six other intelligent algorithms on the Solomon dataset show that the proposed algorithm is superior to other comparative algorithms and has good  search capabilities and application value.

Aiming at the problem that the conventional soft actor-critic (SAC) algorithm lacked exploration capability and state representation in complex environments, we proposed an improved soft actor-critic (ISAC) algorithm. Firstly, the ISAC algorithm  introduced a prioritized experience replay (PER) mechanism, which dynamically evaluated the priority of experience samples by using the temporal differential errors, thereby enhancing the utilization of crucial experiences and improving learning efficiency of the algorithm. Secondly, the algorithm integrated  generative Transformer architecture  into the actor network to strengthen its ability to dynamically capture state features, thereby significantly improving its performance in complex optimization tasks. Finally, we conducted an application experiment  on the dynamic scheduling optimization problem of university logistics staff. The experimental results show that, compared with the original  SAC algorithm and the classic deep Q-network (DQN) algorithm, the proposed ISAC algorithm has smaller errors in dynamically fitting human resource demand, which effectively demonstrates its 
advantages and practicality in practical applications.

Aiming at  the problem that the traditional BIRCH algorithm was prone to excessive intra-cluster variance or excessive merging when dealing with indicator data with strongly correlated features and uneven distribution, we proposed an improved BIRCH algorithm  that integrated an autoencoder and a dynamic threshold strategy. Firstly, this algorithm  utilized an autoencoder for nonlinear feature mapping and dimensionality reduction, weakening the influence of inter-feature correlation on the distance metric and improving the compactness and discriminability of the data representation. Secondly, we designed a dynamic threshold strategy to adaptively adjust the clustering radius based on local sample density and cluster size, enhancing the algorithm’s adaptability to unevenly distributed data. Finally, we  constructed a clustering feature tree by using the improved feature space and adaptive threshold strategy to achieve efficient and stable hierarchical clustering, and applied to intelligent clustering analysis of multidimensional data of university teachers. Experimental results show that the improved algorithm achieves superior performance on multiple clustering evaluation metrics, significantly improving  stability and accuracy of clustering.

Aiming at the problem that malicious Web page links and plugins could be attached to other files through constant confusion and deformation, traditional detection methods were difficult to achieve accurate detection, we proposed a Web page attack redirection confusion detection method based on multimodal deep neural networks. Firstly, we extracted the features of  Web page attacks: attribute class, keyword class, var class, and word class, and converted them into 8-dimensional sensitive feature vectors to 
calculate their corresponding real values. Secondly, the Web page and real values were input together into a multimodal deep neural network for training. Finally, accurate attack redirection confusion detection results were obtained through the output of the Web page classifier. The experimental results show that the detection rate of the proposed method is about 98%, which can effectively detect redirection confusion in Web page attacks while ensuring a high detection rate.

Aiming at the problem that wireless access nodes  in wireless communication networks were affected by changes in network status during communication and found it difficult to quickly adapt to these changes, reconfiguring network resources, and affecting communication efficiency and stability, we proposed an instant equilibrium allocation algorithm for multi node electronic information resource communication. Firstly, based on graph theory, a network communication graph and a conflict graph were constructed, and the communication relationships of each node in the communication network were determined by using the communication graph. The vertex coloring algorithm was used to color the conflict graph, and the orthogonal pairing method was 
used to select the links with the strongest orthogonality in the channel for pairwise pairing,  completing the communication link grouping. Secondly, a balanced allocation model  with the goal of minimizing communication delay and maximizing energy efficiency was established. The reverse differential tunicate swarm algorithm was used to solve the model. Through operations such as mutation, crossover, and selection, the search process of the algorithm was accelerated and optimization efficiency was improved. The optimal solution that met the conditions was found in the shortest number of iterations, resource allocation was completed, and the optimal allocation scheme was ultimately determined. The experimental results show that the highest packet loss of the proposed algorithm is only 3.12%, the lowest communication delay can reach 0.1 ms, and the Jain fairness index is always above 0.9, which can improve the efficiency and stability of the communication network.

Aiming at the problem that the significant disparities in  residual energy among nodes led to uneven energy consumption,  affecting  load balancing, limiting  information transmission efficiency, and  increasing packet loss rates  in wireless sensor networks employing non-uniform clustering, we  proposed a load-balanced non-uniform clustering routing algorithm for wireless sensor networks. Firstly, we used a hybrid energy-efficient distributed clustering protocol to perform non-uniform clustering of nodes in wireless sensor networks,  calculated the clustering probability for each node and selected the node with the highest probability as a candidate cluster head node. Secondly, we designed a node  evaluation function based on  residual energy of nodes and its distance to neighbors, calculated the evaluation function value of each node, elected the  node with the highest evaluation function value as the  cluster head  to construct a cost function,  selected relay nodes to enhance transmission efficiency, and  formed an inter-cluster multi-hop routing algorithm. Finally, we distributed the data transmission tasks to  multiple nodes in the network to  reduce single-node energy consumption and achieve  non-uniform clustering routing load balancing in wireless sensor networks. Experimental results show that  the residual energy of each node in this algorithm  only  fluctuates around 6 J, and the fluctuation amplitude of the curve is small. The network packet loss rate is low at 0.22% when   transmitting 2 000 bit data volumes, indicating high  load balancing.

We proposed a direct measurement schemes for the concurrences of photonic hyperentangled states based on quantum-dot-microcavity coupling system. The hyperentangled states were encoded in the polarization and spatial mode degrees of freedom (DOF) of photons. The schemes for entanglement measurement of both DOFs were constructed by error-heralded controlled-phase-flip gates through the single-photon input-output process of the quantum-dot-microcavity system. By transforming the concurrences into the detection probabilities of odd parity state, the schemes achieved efficient measurement of the concurrences of hyperentangled states. The schemes could not only independently measure the concurrence in each DOF, but also overcome the quantum operation distortions caused by cavity loss and imperfect coupling in traditional schemes. The research results show that the schemes have high experimental feasibility and robustness, providing a new approach for measuring hyperentangled states in quantum information processing.

Aiming at the problem that the copper component in the neutralization gun of X-ray photoelectron spectroscopy was extremely easy to be contaminated and corroded, taking the Thermo Scientific NEXSA type X-ray photoelectron spectroscopy as an example, by studying the working mechanism and structural properties of the neutralization gun, and combining with the scanning electron microscope and energy dispersive spectrometer to analyze the contamination on the surface of the corroded copper mesh, we proposed an improved method of electroplating inert metal film on the copper mesh. By comparing the surface contamination
 of copper and gold standard samples built in the instrument under the long-term test environment in the analysis chamber through the full spectrum scanning test, we determined the coating material and process, and conducted performance test of the improved neutralization gun. The results show that the gold electroplating on copper mesh does not affect the normal use of the neutralization gun, the improved neutralization gun still has a good neutralization effect on insulating samples, and the service life can be increased by more than 5 times of that before improvement, greatly improving its corrosion resistance performance.

We used femtosecond laser processing technology to improve the optical absorption rate of SiC in the infrared band (especially within the 10.3~12.6 μm range), in order to solve the problem of traditional processing techniques being difficult to finely process and having low absorption rates. We used femtosecond laser direct writing technology to generate specific micro/nanostructures on the surface of SiC by adjusting key parameters of laser processing, and analyzed the surface morphology and optical properties of the processed samples by using scanning electron microscopy and Raman spectrum. The results show that the surface morphology of SiC can be effectively modulated through femtosecond laser processing, and its infrared absorption rate is significantly improved, with a maximum absorption rate of 92%. The nanostructures can reduce the reflectance of materials and enhance the excitation of surface phonon polaritons, thereby enhancing the infrared light absorption capacity of materials.

Aiming at the problems of weak electromagnetic interference immunity, continuous external power supply, complex installation process, low signal-to-noise ratio, and insufficient sensitivity of conventional power grid dance monitoring systems, we proposed a novel cable disturbance monitoring system. The system employed a dual-ended Mach-Zehnder interferometric (MZI) optical path structure, which could achieve long-distance, large-scale, and multi-dimensional online monitoring and structural safety warning to locate the position of the dance in real-time. The sensor core adopted a thin-walled sensitivity-enhanced cable sleeve design, which integrated a laser MZI optical path composed of high-sensitivity micro-optical fiber and couplers inside. This interferometer had excellent response characteristics to vibration. After being encapsulated within a specialized metal housing to form an integrated dance monitoring sensor. The experimental results show that the natural frequency of the finite element of the sensor is 106.77 Hz, and the relative error with the measured date is only 1.65%. The relative sensitivity of the detector in the range of 0—140 Hz is 41.25—66.78 dB(rad/Pa), which confirms its ability to detect the high sensitivity of the dance signal.

We studied  the mechanism of the reaction between 2α-Ala→Mg²⁺ (bis-alanine chelating magnesium)  and  ^.OH (hydroxyl radical) in the aqueous phase environment of living organisms (1.013×10⁵ Pa,  310.15 K) at the level of M06-2X/6-311+G(d,p)//MN15/6-311++G(3df,2pd)  theory, and investigated two reaction channels of  2α-Ala→Mg²⁺ and ^.OH for the hydrogen abstraction and addition. The calculation results show   that the energy barrier for the hydrogen abstraction reaction is from 20.1 to 62.3 kJ/mol,  all of which are exothermic reactions. The energy barrier for the addition reaction is from 65.7 to 70.9 kJ/mol,  with a slight endothermic reaction. Therefore,  2α-Ala→Mg²⁺ in living organisms can easily scavenge ^.OH by abstracting H atoms.

Rare-earth small molecule chelator  was used to prepare antibody markers of severe acute respiratory syndrome coronavirus 2(SARS-CoV-2), and SARS-CoV-2 antigen was detected by time-resolved fluorescence immunochromatography. The experimental results show that the linear range of the method is 0.04—100 ng/mL,  the linear equation is y=0.007 2x+0.033 2, the correlation coefficient R²=0.999 5. The detection limit is 0.028 ng/mL. The intra-assay and inter-assay coefficients of variation are less than 6.72%,  and the recovery rate is  94.35%—103.00%. The method has the advantages such as good precision,  low detection time (less than 20 min),  low cost,  and simple operation.

We used laboratory simulation methods  to investigate the effects of freeze thaw (FT) and microplastics on transformation of arsenic (As) speciation in  soil. The results show that under the condition of not adding microplastics,  FT leads to an increase in the proportions of organic-bound As and weakly crystalline iron oxide-bound As (3.67% and 4.17%),  while the proportion of manganese oxide-bound As and extremely difficult to  crystallize iron oxide-bound As decreases (0.28% and 5.33%). Adding polyethylene (MP-PE) under FT can reduce the proportion of organic-bound As (0.96%), increase th proportion of manganese oxide-bound As,  sulfide-bound As,  and crystalline iron oxide-bound As(1.55%,  0.60%,  and 2.05%). Adding butylene adipate-co-terephthalate (MP-PBAT) under FT can reduce the proportion of water-soluble As and crystalline iron oxide-bound As (1.33% and 2.65%),  and increase the proportion of  manganese oxide-bound As and extremely difficult to  crystallize iron oxide-bound As (1.11% and 3.82%). Under the condition of not adding microplastics, FT significantly increases the bounding strength coefficient IR between As and soil by 1.85%, but  adding MP-PBAT under FT, IR significantly decreases by 6.27%. The IR value is positively correlated with water-soluble As,  organic-bound As,  and manganese oxide-bound As, and  negatively correlated with the effect of the crystalline iron oxide-bound As. The research results  provide theoretical  basis for revealing  the environmental behavior of As in contaminated soils and evaluating the  ecological risks of As, and provide important  reference value   for the treatment and risk management of As-contaminated soil.